Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

Streszczenie

We prove that if $ \mathcal {C} $ is a family of separable Banach spaces which is analytic with respect to the Effros Borel structure and no $ X \in \mathcal {C} $ is isometrically universal for all separable Banach spaces, then there exists a separable Banach space with a monotone Schauder basis which is isometrically universal for $ \mathcal {C} $ but not for all separable Banach spaces. We also establish an analogous result for the class of strictly convex spaces.